Constraining the derivation of alternatives

Nat Lang Semantics (2015) 23:249–270DOI 10.1007/s11050-015-9115-y

Constraining the derivation of alternatives

Tue Trinh1 · Andreas Haida2

Published online: 13 June 2015© Springer Science+Business Media Dordrecht 2015

Abstract Inferences that result from exhaustification of a sentence S depend on theset of alternatives to S. In this paper, we present some inference patterns that are prob-lematic for previous theories of alternatives and propose some structural constraintson the derivation of formal alternatives which derive the observations.

Keywords Alternatives · Exhaustification · Implicature · Focus · Symmetry

1 Introduction

One way to describe the strengthened meaning of a sentence S, i.e. the conjunctionof its literal meaning and its implicature, is to say that S can be parsed as exh(A)(S),where A is a set of alternatives of S and exh an exhaustifying operator which maps Aand S to true iff S is true and the elements of a subset of A, defined relative to S andA, are false (cf. Krifka 1995; Fox 2007a; Chierchia et al. 2012; Magri 2009, 2011;among others).1

1 Following Fox (2007a,b), we assume N(S,A) in (1) to be the set of “innocently excludable alternativesin A given S,” defined as follows:

(i) N(S,A) := ∩ {A′ | A′ is a maximal subset of A such that {S} ∪ {¬S′ | S′ ε A′} is consistent}

B Andreas [email protected]

Tue [email protected]

1 Department of Linguistics, University of Wisconsin - Milwaukee, Curtin Hall 535, P.O. Box 413,3243 N. Downer Ave., Milwaukee, WI 53211, USA

2 Department of English and American Studies, Humboldt-Universität zu Berlin,Unter den Linden 6, 10099 Berlin, Germany

123

http://crossmark.crossref.org/dialog/?doi=10.1007/s11050-015-9115-y&domain=pdf

250 T. Trinh, A. Haida

(1) exh(A)(S) = S ∧ ∧{¬S′ | S′ ε N(S,A)}

Under this perspective, predicting the strengthened meaning of S involves predictingwhat is in A. For example, we predict (2a) to have the strengthened meaning in (2b)if we predict (2c).

(2) a. exh(A)(John did some of the homework)b. John did some of the homework ∧ ¬John did all of the homeworkc. A = {John did some of the homework, John did all of the homework}

Ashas beennoted, this approach to implicature amounts to assimilating it to associationwith focus (cf. Krifka 1995; Fox 2007b; Fox and Katzir 2011). The definition of exhis essentially that of the exhaustifying operator only, modulo the fact that only(A)(S)presupposes the prejacent instead of asserting it.2

(3) only(A)(S) = exh(A)(S) if |�c S, undefined otherwise

For present purposes, we can ignore the difference between presupposition and asser-tion and regard only simply as the overt counterpart of exh. The strengthenedmeaningof (2) can then be identified with the literal meaning of (4).3

(4) John only did some of the homework

Wewill consider exh(A)(S) and only(A)(S) two different instances of themore generalphenomenon of exhaustification of S, and use “EXH” as a cover term for exh and only.The aim of this paper is to propose a characterization ofAwhich accounts for inferencepatterns of EXH(A)(S) that pose a challenge for other proposals. An example of suchpatterns is the paradigm below.

(5) Bill went for a run and didn’t smoke. John (only) went for a run.Inference: ¬[John went for a run and didn’t smoke]

(6) Bill passed some of the tests and failed some. John (only) passedsome of the tests.*Inference: ¬[John passed some of the tests and failed some]

Footnote 1 continuedInformally, then, N(S,A) is the intersection of all maximal subsets of A whose elements can be consistentlynegated in conjunction with S.Wewill leave it to the reader to do the computations to see how this definitionworks with respect to the examples discussed in the text.The operator exh can be seen as a notational device expressing pragmatic reasoning on a sentence (cf.

Sauerland 2004; Spector 2006), or alternatively as a grammatical device which is syntactically representedand interpreted by compositional semantics. We believe the second option is correct, in light of argumentsmade elsewhere concerning free choice disjunction (Fox 2007a), Hurford’s Constraint (Chierchia et al.2012), modularity (Magri 2009, 2011), and intermediate implicatures (Sauerland 2012). The precise statusof exh, however, will not be essential for what follows.2 The ‘prejacent’ is the sentential argument of exh.3 Embedding (4) under exh will have no semantic effect, so we may assume that sentences are by defaultconstrued with exh (cf. Fox 2007a). This raises the issue of the distributional differences between only andexh, which we will also have to ignore (cf. Crnic 2012 and references therein).

123

Constraining the derivation of alternatives 251

While (5) can be understood to mean that what is true of Bill is not true of John, (6)cannot.4 Specifically, (5) can imply that it is not the case that John went for a run anddidn’t smoke (i.e. that John smoked) but (6) cannot imply that it is not the case thatJohn passed some of the tests and failed some (i.e. that John passed all of the tests). Asfar as we know, this contrast has not been noted in the literature, and is not predictedby any theory of alternatives on the market.

The paper is structured as follows. The rest of Sect. 1 sets up the backgroundfor the subsequent discussion. Section 2 introduces the central empirical puzzle whichmotivates our account. Section 3 presents a resolution of this puzzle. Section 4 extendsthe hypothesis proposed in Sect. 3 to solve other problems. Section 5 is the summary.

1.1 Relevance

Rooth (1992) notes that EXH(A)(S) licenses different inferences depending on whichconstituent of S is focused (i.e. F-marked). He consequently proposes that A beregarded as F(S) ∩ C, where F(S) is the set of formally defined alternatives of Sand C the set of pragmatically salient sentences. Rooth defines F(S) as follows.

(7) Formal alternatives (Rooth 1992)F(S) = {S′ | S′ is derivable from S by replacement of F-marked constituentswith expressions of the same semantic type}

Fox and Katzir (2011; henceforth F&K) argue that C should be identified with the setof relevant sentences, where relevance is to be closed under negation and conjunction.5

(8) Closure conditions on C (Fox and Katzir 2011)(i) If p ε C, then ¬p ε C.(ii) If p ε C and q ε C, then p ∧ q ε C.

1.2 Symmetry

The conception of A as F(S) restricted by relevance leads to a problem with Rooth’sdefinition of F(S): the so-called “symmetry problem.”6 As an illustration, consider(9), with the parse indicated.

4 The sequence in (6) is admittedly odd. Our intuition is that the reason for its oddness is precisely thatit cannot mean that what is true of Bill is not true of John. To the extent that our intuition is correct, theproblem at hand can be framed as one of explaining the contrast in acceptability between (5) and (6).5 These two closure conditions follow from the assumption that to be relevant is to distinguish exclusivelybetween answers to the “question under discussion.” More explicitly, let Q be the question under discussionand Ans(Q)(w) be the set of answers to Q that are true in w. For a proposition p to be relevant, it must holdthat p makes no distinction between w and w′ if there is no distinction between Ans(Q)(w) and Ans(Q)(w′),i.e. it must hold that p(w) = p(w′) if Ans(Q)(w) = Ans(Q)(w′) (cf. Groenendijk and Stokhof 1984; Lewis1988; von Fintel and Heim 1997).6 The symmetry problem was first formulated in the context of the discussion of scalar implicatures (Kroch1972; von Fintel and Heim 1997). However, it generalizes to association with focus, as shown in Fox andKatzir (2011).

123


(9) John (only) has threeF chairsEXH(A)(S), where S = John has three chairs

By hypothesis, both S′ = John has four chairs and S′′ = John has exactly threechairs are in F(S), as four and exactly three are both of the same semantic type asthree. And given that S is relevant, S′ is in C if and only if S′′ is in C.7 Thus, A = F(S)∩ C contains either both S′ and S′′ or neither of these alternatives, which means that(9) cannot license ¬S′ as an inference, because this inference requires that A containS′ but not S′′. In actuality, however, this is exactly the inference we draw from (9): thesentence clearly implies that John has three chairs and not four.

Some other examples of the same sort are given below. In each case, the twoalternatives S′ and S′′ are such that either both are predicted to be in A or none is. Andin each case, ¬S′ is the observed inference.

(10) John (only) [did some of the homework]FS′ = John did all of the homework, S′′ = John did some but not all of thehomework

(11) John (only) [talked to Mary or Sue]FS′ = John talked to Mary and Sue, S′′ = John talked to Mary or Sue but notboth

Such alternatives as S′ and S′′ in the examples above are called ‘symmetric alterna-tives’. More explicitly, we say that S′ and S′′ are symmetric alternatives of S if (i)S′ ∧ S′′ is a contradiction and (ii) S′ is relevant iff S′′ is relevant. The “symmetryproblem” is this: A is predicted to contain either both S′ and S′′ or none of these, whilethe facts require that A contain S′ but not S′′. This problem is solved by “breakingsymmetry,” i.e. by redefining A in such a way that it can contain S′ but not S′′.

1.3 Complexity

Building on Katzir (2007, 2008), F&K advance a theory of alternatives which startsfrom the intuition that what distinguishes between the symmetric alternatives above istheir structural complexity: S′′ is more complex than S while S′ is not. To exclude S′′from A, then, F&K propose to reduce the set of formal alternatives from the Roothianset, which we will henceforth denote with ‘FRooth(S)’, to a proper subset of this setwhich contains only structures that are (considered by the discourse participants to be)“no more complex” than the prejacent.

(12) Formal alternatives (F&K)F(S) = FRooth(S) ∩ {S′ | S′ �c S}

The relation ‘x �c y’ holds between linguistic expressions in general and is to beunderstood as ‘x is no more complex than y in discourse context c.’ Here is thedefinition:

7 Thus, if S′ ε C, then ¬S′ ε C, which means S∧¬S′ ε C, which means S′′ ε C, as S′′ ≡ S∧¬S′. The sameargument can be made with S′′ in place of S′.

123


(13) Complexity metric (F&K)a. E′ �c E if E′ = Tn(…T1(E)…), where each Ti (x) is the result of replacing

a constituent of x with an element of SS(E,c), the substitution source of Ein c

b. SS(E,c) = {x | x is a lexical item} ∪ {x | x is a constituent uttered in c}Basically, E′ is no more complex than E if E′ can be derived from E by a series ofsubstitution transformations, each of which applies to an input x and replaces oneconstituent of x with a lexical item or a constituent uttered in the context.8 The readercan verify for herself that F&K’s complexity metric correctly predicts S′, but not S′′,to be a formal alternative of S in (9), (10), and (11). This metric also accounts for factsbeyond those we have considered, such as the contrast between (14) and (15).

(14) Yesterday it was (only) warm. Today it is warm and sunny with gusts of wind.Inference: ¬Yesterday it was hotInference: ¬Yesterday it was warm and sunny with gusts of wind

(15) Yesterday it was (only) warm.Inference: ¬Yesterday it was hot*Inference: ¬Yesterday it was warm and sunny with gusts of wind

While (14) implies that it was not hot and also that it was not sunny with gusts of wind,(15) only licenses the inference that it was not hot. This is because in the case of (14),alternatives can be generated by replacing warm with hot, taken from the lexicon,and with warm and sunny with gusts of wind, taken from the discourse context,while in the case of (15) the second replacement is not an available option. Thus, whatis uttered in the context affects the domain of EXH and hence the inference of theexhaustified sentence. Several additional supporting data are given in Katzir (2007)and Fox and Katzir (2011). Here is one more example, taken from Fox and Katzir(2011) with slight modification.

(16) Detective A concluded that the robbers stole the book and not the jewelry.Detective B (only) concluded that they stole the book.Inference: ¬Detective B concluded that the robbers stole the book and not thejewelryInference: ¬Detective B concluded that the robbers stole the book and thejewelry

The first inference comes about by way of the alternative in (17a), which is generatedby replacing the book in the prejacent with the book and not the jewelry. The secondinference comes about by way of the alternative in (17b), which is derived from thefirst alternative, (17a), by replacing not the jewelry in (17a) with the jewelry.

(17) a. Detective B concluded that they stole the book and not the jewelryb. Detective B concluded that they stole the book and the jewelry

8 It follows from this definition that E �c E, i.e. that an expression is no more complex than itself.

123


Thus, F&K assume that alternatives can be derived by “successive replacement” inthe sense that a constituent α can be replaced by another constituent β which can itselfbe altered by further replacements.9

A prominent advantage of F&K’s theory is that it derives the right alternatives fordisjunction in the same manner as other alternatives are derived, i.e. by substitution.Consider (18).

(18) John is (only) required to read the book or do the homework.Inference: ¬John is required to read the bookInference: ¬John is required to do the homework

The alternatives necessary for these inferences are derived by replacing read the bookor do the homework in the prejacent with read the book in one case and with dothe homework in the other.

2 Identifying the problem: unexpected symmetry breaking

In the theory of alternatives proposed by F&K, symmetry is broken exclusively inF(S): the problematic symmetric alternative is excluded from A = F(S) ∩ C by condi-tions imposed on F(S), not on C. This aspect of F&K’s proposal reflects a convictionunderlying most semantic analyses which appeal to alternatives.

(19) Standard view on symmetrySymmetry can only be broken formally.

Let us, at this point, introduce the main empirical puzzle that this paper sets out toresolve. This puzzle can be divided into two parts. The first concerns data such as(20a–c), which seem to contradict the standard view on symmetry.

(20) a. Bill went for a run and didn’t smoke. John (only) went for a run.Inference: ¬[John went for a run and didn’t smoke]

b. Bill works hard and doesn’t watch TV. John (only) works hard.Inference: ¬[John works hard and doesn’t watch TV]

c. Bill is tall and not bald. John is (only) tall.Inference: ¬[John is tall and not bald]

All of these sentences license the inference that what is true of Bill is not true ofJohn. For example, (20a) implies that it is not the case that John went for a run anddidn’t smoke (i.e. that he smoked). Given what has been said, however, this inferenceis licensed only if symmetry can be broken outside of F(S). Thus, (20a) has the formEXH(A)(S) where S = John went for a run. The formal alternatives of S in thiscase include both S′ = John went for a run and didn’t smoke and S′′ = John went

9 This is what we take F&K to mean by “successive replacement,” as we see no other way to derive (17b)(see Katzir 2007, p. 679; Fox and Katzir 2011, pp. 97, 103). Of course, this does not mean the attestedinferences require such an understanding of “successive replacement,” as we will argue below.

123


for a run and smoked, which are symmetric alternatives.10 The attested inference,however, is that John smoked, which is only possible if A contains S′ but not S′′. Thus,we have a case where F(S) contains symmetric alternatives while A does not, i.e. acase where, on F&K’s definition of F(S), symmetry is broken outside of F(S).

The same holds for (20b) and (20c). In (20b), the set of formal alternatives to S =John works hard, which is the prejacent of EXH, contains both John works hardand doesn’t watch TV and its symmetric counterpart John works hard and watchesTV. Given that EXH(A)(S) implies that it is not the case that John works hard anddoesn’t watch TV (i.e. that he watches TV), A must be such a restriction of F(S) as tocontain the first but not the second alternative. In other words, A must be a symmetrybreaking restriction of F(S). Similarly, the set of formal alternatives to the prejacentof EXH in (19c), which is S = John is tall, contains both John is tall and not baldand the symmetric counterpart John is tall and bald, but the inference attested forEXH(A)(S), namely that it is not the case that John is tall and not bald (i.e. that heis bald), is only possible if A contains the second but not the first alternative, i.e. ifsymmetry is broken outside of F(S).

The observations in (20), then, suggest that the standard view on symmetry is false.It turns out, however, that there is another set of data which has a very similar structureto that in (20) butwhich leads to the exact opposite conclusion, namely that the standardview on symmetry is correct. This is the second part of the puzzle.

(21) a. Bill ate exactly three cookies. John (only) ate three cookies.*Inference: ¬John ate exactly three cookies

b. Bill fathered children and no twins. John (only) fathered children.*Inference: ¬[John fathered children and no twins]

c. Bill passed some of the fitness tests and failed some. John (only) passedsome of the fitness tests.*Inference: ¬[John passed some of the fitness tests and failed some]

In (21a), the prejacent of EXH is S = John ate three cookies, and the set of formalalternatives of S, F(S), includes both John ate four cookies and John ate exactlythree cookies. The fact that EXH(A)(S) cannot imply that it is not the case that Johnate exactly three cookies (i.e. that John ate more than three cookies) means that F(S)cannot be restricted to a set A which contains John ate exactly three cookies butnot its symmetric counterpart. In (21b), the prejacent of EXH is S = John fatheredchildren, and F(S) contains both John fathered twins and its symmetric counterpartJohn fathered children and no twins. The fact that EXH(A)(S) cannot imply thatJohn fathered twinsmeans thatA cannot eliminate one alternative fromF(S) but not theother. Similarly, the prejacent of EXH in (21c) is S = John passed some of the fitnesstests, and F(S) contains both John passed all of the fitness tests and its symmetriccounterpart John passed some of the fitness tests and failed some. The fact thatEXH(A)(S) cannot imply that it is not the case that John passed some of the fitness

10 The first alternative S′ is generated by replacing went for a run in S with went for a run and didn’tsmoke, taken from the discourse context. The second alternative S′′ is generated by replacing didn’tsmoke in S′ with smoked, also taken from the discourse context. As S is relevant and S′ ≡ S ∧ ¬S′′ andS′′ ≡ S ∧ ¬S′, S′ is relevant iff S′′ is.

123


tests and failed some (i.e. that he passed all of the fitness tests) means that A cannotbreak symmetry by restricting F(S) to a set which contains the second alternative tothe exclusion of the first.

Here, then, is the problem facing us. We have a definition of F(S) and a definitionof A which together imply that if F(S) contains two symmetric alternatives S′ and S′′,A must contain both S′ and S′′ and consequently EXH(A)(S) cannot imply¬S′. In thissection, we have examined cases where F(S), by definition, contains two symmetricalternatives S′ and S′′. In some of these cases, EXH(A)(S) can imply ¬S′ while insome others it cannot. The task, therefore, is to establish a distinction between thesetwo sets of cases which matches the attested inference patterns.

3 Solving the problem

3.1 First attempt: relying on pragmatic scales alone

One strategy that readily comes tomind is to appeal to the notion of a “pragmatic scale”(cf. Klinedinst 2004). To illustrate, let us consider (22a) and (22b), as representativesof cases where symmetry can and cannot be broken outside of F(S), respectively.


b. Bill passed some of the fitness tests and failed some. John (only) passedsome of the fitness tests.*Inference: ¬[John passed some of the fitness tests and failed some]

Given common knowledge, it seems much easier to construct an evaluative scale onwhich running and smoking is ranked lower than running and not smoking, for exampleone which measures the degree of healthiness, than it is to construct a scale on whichpassing all of the tests ranks lower than passing some but not all of the tests. Suppose,then, that symmetry can in principle be broken in C, or equivalently that EXH(A)(S)can in principle license ¬S′ as an inference even though F(S) contains both S′ and itssymmetric counterpart.11 In addition, suppose we say that in such discourse contextsas those in (22), EXH(A)(S) can only license ¬S′ as an inference if S∧ ¬S′ is rankedlower than S ∧ S′ on some pragmatic scale. It will then seem that we can account forthe contrast between (22a) and (22b). Thus, the prejacent S of EXH in (22a) is Johnwent for a run and the relevant alternative S′ is John went for a run and didn’tsmoke. The reason EXH(A)(S) can imply ¬S′ in this case would be that there is apragmatic scale measuring the degree of healthiness on which S ∧ ¬S′, which saysthat John went for a run and smoked, is ranked lower than S ∧ S′, which says thatJohn went for a run and didn’t smoke. For (22b), where S = John passed some of

11 Let it already be said at this point that we will end up abandoning this attempt of having symmetry bebroken in C and will come back to assuming F&K’s claim that symmetry can only be broken in F. Notethat if we were to pursue the hypothesis that symmetry can in principle be broken in C, we would have toaddress F&K’s empirical arguments to the contrary, most probably by showing that the relevant pragmaticscales are missing in the cases that F&K discuss.

123


the fitness tests and S′ = John passed some of the fitness tests and failed some,EXH(A)(S) cannot license ¬S′ as an inference because there is no pragmatic scaleon which S ∧ ¬S′, which says that John passed all of the tests, is ranked lower thanS ∧ S′, which says that John passed some but not all of the tests.

An account along this line is also supported by the following contrast.12


b. Bill went for a run but didn’t lift weight. John (only) went for a run.*Inference: ¬[John went for a run and didn’t lift weight]

We can see that changing (23a) into theminimally different (23b) results in the absenceof the inference that what is true of Bill is not true of John. As the change consistssolely in replacing the “positive” property of not smoking with a “negative” propertyof not lifting weight (and the concomitant replacement of and with but), we haveevidence that the availability of an appropriate pragmatic scale, however the detailsof the account will be worked out, plays a role in licensing the type of inferencesobserved in such sentences as (23a).

It turns out, however, that the pragmatic scale approach,while it promises to accountfor the contrast in (23), seems hopeless as an explanation for the difference betweenthe two sets of cases presented in the last section. Specifically, it turns out that even ifwe make available, and salient, a pragmatic scale on which passing all of the fitnesstests is ranked lower than passing some and failing some, (22b) still cannot licensethe inference that it is not the case that John passed some and failed some of the tests.Thus, imagine a situation where everyone has to take military fitness tests and thosewho pass all of these tests must join the army and go to the frontline to be slaughteredby the enemy while those who fail some of the tests can stay home and go to college.In this draft dodging context, a scale which measures the degree of luck will be oneon which passing all of the military fitness tests is ranked lower than passing someand failing some of these tests. But it seems that even this context cannot support therelevant inference for (22b).

(24) Bill has once again been dealt a better hand than John. He passed some of themilitary fitness tests and failed some, while John (only) passed some of thetests.

We believe that (24) cannot license the inference that it is not the case that John passedsome of the military fitness tests and failed some, i.e. that he passed all of the tests.

Let us now look at the other examples in (21) to convince ourselves that the prag-matic scale account does not hold water. For (21a), imagine a “gluttony rehab” contextwhere eating fewer cookies means making more progress. In this context, there is apragmatic scale on which eating more than three cookies is ranked lower than eatingexactly three cookies, namely one which measures how far a person is from being aglutton. Again, it appears that even this context does not help in getting the following

12 Apparently, the absence of the inference that John is different from Bill with respect to running andlifting weights makes (23b) sound a bit odd (see footnote 4).

123


sentence to imply that John ate three but not exactly three cookies, i.e. that he ate morethan three cookies.

(25) Bill is making more progress at the gluttony rehab center than John. Today heate exactly three cookies, while John (only) ate three cookies.

A similar argument can be made for (21b). Imagine a fictional “genetic lab” contextwhere scientists try to engineer the most “representative” maleHomo sapiens, i.e. onewhich can father children but which does not have the biological defect of alwaysfathering (identical) twins.13 In this context, a scale measuring how similar an engi-neered sample is to the majority of naturally born humans would rank a specimenwhich fathered twins lower than one which fathered children but no twins. However,it seems that even this context fails to enable the following sentence to imply that Johnfathered twins.

(26) Bill turned out to be a better specimen than John. He fathered children and notwins, while John (only) fathered children.

We conclude that a solution to the problem identified in Sect. 2 in terms of pragmaticscales is not tenable.14 Let us try another route.

3.2 Second and final attempt: syntactic atomicity

Let us start with a reformulation of F&K’s theory which will facilitate the presentationof the problem it faces. Given the assumption that the prejacent is always relevant andthat the set C of relevant sentences is closed under negation and conjunction, F&K’shypothesis that A = F(S) ∩ C amounts to the hypothesis that A is a set which satisfiesthe following three conditions.15

(27) Conditions on A (F&K)a. A ⊆ F(S)

b. S is in A.c. There is no S′ in F(S)\A such that S′ is in the Boolean closure of A.

Informally speaking, A is the set of all and only those sentences in F(S) that areconsidered relevant, which means that if a sentence ϕ is in A, then every sentence in

13 Let us, for argument’s sake, assume that the male parent can be responsible for monozygotic twinning.14 More precisely, the discussion in this section shows that the availability of an evaluative scale on whichS ∧ ¬S′ is ranked lower than S ∧ S′ is not sufficient for the inference ¬S′ to arise. Still, the contrast in(23) suggests that the availability of such a scale is a necessary condition: the inference does not arise inthe case of (23b) because the conjunction but in the context sentence presupposes or implicates a scale onwhich running and not lifting weights (S ∧ S′) is ranked lower than running and lifting weights (S ∧ ¬S′).15 Note that F&K actually end up proposing a revision of the last condition: there is no S′ in F(S)\A suchthat EXH(A)(S′) is in the Boolean closure of A. The revision is motivated by a problem with disjunction,specifically the problem of ensuring that if a disjunction is relevant then both disjuncts are (cf. Fox andKatzir 2011 for details). It turns out, however, that this problem can be solved by other means (cf. Spector2010). The difference between the original and the revised condition on A is immaterial for our discussion.

123


F(S) that becomes relevant by virtue of ϕ and other sentences in A being relevant mustalso be in A.

We now turn to a more explicit discussion of the challenge confronted by F&K’stheory, i.e. the cases of symmetry being broken outside of F(S). Let us again take(20a), repeated in (28) below, as a representative of these cases.


It follows from F&K’s definition of formal alternatives that F(S), with S = John wentfor a run, is the set in (29).16

(29) {run, smoke, ¬run, ¬smoke, run ∧ ¬smoke, run ∧ smoke}

The attested inference of John went for a run, namely that John smoked, requiresthat the domain A of EXH, assuming it is a subset of F(S) which contains S, be any ofthe three sets in (30). Thus, EXH(30a)(run) = EXH(30b)(run) = EXH(30c)(run) =run ∧ smoke.

(30) a. {run, run ∧ ¬smoke, ¬run, ¬smoke}b. {run, run ∧ ¬smoke, ¬run}c. {run, run ∧ ¬smoke}

The problem, however, is that none of the sets in (30) satisfies the last condition onA in (27), given that F(S) = (29).17 To see this, let X be any of these sets. It will thenhold that (29)\X contains run ∧ smoke which, being equivalent to run ∧ ¬(run ∧¬smoke), is in the Boolean closure of X.

16 To be explicit, we assume the following constituent structures for the two sentences in question. Thereader can verify for herself that (29) is the set of formal alternatives of (i-b), according to F&K’s definition.

(i) a. TP

DP

Bill

T

T

T

PAST

VP

go for a run

and T

T

PAST

NegP

Neg

not

VP

smoke

b. TP

DP

John

T

T

PAST

VP

go for a run

Importantly, F&K predict that neither ¬(run ∧ smoke) nor ¬(run ∧ ¬smoke) is a formal alternative of(i-b), as none of these can be generated by successively replacing constituents of (i-b) with constituents of(i-a) or (i-b).17 However, note in advance that the last condition in (27) can be satisfied if smoke is excluded from A:smoke is not in the Boolean closure of the sets in (30b) and (30c).

123


3.2.1 The Atomicity constraint

The solutionwepropose to the problemcreated by the example above for F&K’s theoryconsists in constraining the derivation of formal alternatives in such a way that F(S)does not contain run ∧ smoke.Wewill present our proposal in two steps: (i) presentingthe constraint on F(S) which excludes run ∧ smoke from this set; (ii) showing howthis constraint works with respect to the example above and other examples that wehave discussed. Let us begin with the first step.

Whatwewant is to exclude run∧ smoke fromF(S),withS=John went for a run.18

Oneway to achieve this goal is to impose onF(S) the condition that all of itsmembers bederivable fromS in atmost one step. Thiswould exclude the derivation of run ∧ smokefrom the prejacent, which necessarily involves two steps. This derivation is shown in(31). By assumption, the relevant substitution source includes the T constituent α =went for a run and didn’t smoke and the VP constituent β = smoke, both of whichhave been uttered in the context.19

(31) Derivation of John went for a run and smoked:0. John went for a run the prejacent1. John went for a run and didn’t smoke T / α2. John went for a run and smoked NegP / β

Imposing on F(S) such a condition, however, will cost us an elegant solution to thenotorious problem of multiple disjunctions, i.e. sentences of the form (A or (B or C)),which by default license the inference that exactly one disjunct is true. This inferencefollows from (the definition of EXH and) the assumption that (A and B), (A and C),and (B and C) are all formal alternatives of (A or (B or C)). But none of these formalalternatives can be generated in one step: each of them requires a step which replacesor with and and another step which reduces the ternary coordination to a binary one,in either order.20 For example, (A and B) is derived from (A or (B or C)) by firstreplacing (B or C) with B and then replacing or in the result with and.

We believe this is good reason for not imposing on F(S) the condition that itselements be derived in at most one step. The question, then, is what makes run ∧smoke special other than the plurality of steps its derivation involves. Our answer willrequire the introduction of a new concept, that of a “syntactically atomic expression,”which in turn requires a brief discussion of what we have been calling the “substitutionsource.”

The substitution source can be naturally thought of as a set of expressions providedby the discourse context for the contruction of formal alternatives. Thus, the syntacticderivation of alternatives “begins”with the substitution source inmuch the sameway as

18 Note that the computations we are looking at for S = John went for a run are all performed in a contextwhere the sentence Bill went for a run and didnt smoke has been uttered.19 See footnote 16. We write “A/B” to denote the result of replacing A in the previous line with B.20 More precisely, the generation of these alternatives requires a step which reduces a structure containingtwo binary coordinations (i.e. (A or (B or C))) to a structure containing only one binary coordination (e.g.(A or B)). Note that a genuine ternary structure such as (A or B or C) cannot be reduced to (A or B) usingF&K’s procedures. We thank Roni Katzir for pointing out this subtle difference.

123


the syntactic derivation of sentences begins with the numeration (cf. Chomsky 1995).One manifest difference between these two contructs, of course, is that whereas thenumeration contains only lexical items, the substitution source contains both lexicalitems and complex phrases. Interestingly, the core of our solution to the problem athand will be the hypothesis that this difference is only phonological, not syntactic.Specifically, we propose the following.

(32) AtomicityExpressions in the substitution source are syntactically atomic.

Basically, the Atomicity constraint states that expressions in the substitution sourcecannot have their proper parts replaced by other expressions in the derivation. Oneway to implement this idea is to say that every expression in the substitution source isformally marked with a feature, AT, which makes it syntactically atomic, i.e. makes itsinternal structure invisible and thus inaccessible to syntactic rules. The numeration andthe substitution source are now similar in the sense that both contain only syntacticallyatomic expressions.

Returning to our example, we now say that the substitution source of John wentfor a run in the relevant discourse context includes α = [AT went for a run and didn’tsmoke] and β = [AT smoke], with each expression now explicitly marked as beingsyntactically atomic. Let us look at the derivation of run ∧ smoke again.

(33) Derivation of John went for a run and smoked:0. John went for a run the prejacent1. John [AT went for a run and didn’t smoke] T / α2. John [AT went for a run and [AT smoked]] *NegP / β

As we can see, the second step in (33) violates Atomicity: it replaces a proper partof a syntactically atomic expression with another expression. This means that run ∧smoke cannot be derived from the prejacent, i.e. that it is not in F(S)—which is theresult we want.21

3.2.2 Deriving the symmetry breaking cases

Let us first consider the “symmetry breaking” cases, i.e the examples in (20), startingwith the one we have been discussing in detail above.


With Atomicity imposed on F&K’s concept of formal alternatives, F(John went for arun) is now the set in (35), as neither ¬run nor run ∧ smoke can be derived withoutviolating the Atomicity constraint.

21 The reader is invited to verify for herself that Atomicity does not create a problem with multiple disjunc-tions, i.e. that we can derive (A and B), (A and C), and (B and C) from (A or (B or C)) without violatingAtomicity.

123


(35) F(S) = {run, smoke, ¬smoke, run ∧ ¬smoke}

The set A, which is the domain of EXH, can now be (36), which satisfies all of theconditions in (27): (i) (36) ⊆ F(S), (ii) run ε (36), and (iii) no member of F(S)\(36) ={smoke, ¬smoke} is in the Boolean closure of (36).

(36) A = {run, run ∧ ¬smoke}

Consequently, EXH(A)(S) = run ∧ ¬(run ∧ ¬smoke), which is the empiricallycorrect result.

Let us now turn to the other symmetry breaking examples in (20) to convinceourselves that the theory works for these cases as well.

(37) Bill works hard and doesn’t watch TV. John (only) works hard.Inference: ¬[John works hard and doesn’t watch TV]

It follows from Atomicity that the set of formal alternatives to S = John works hardin this case is (38a). The domain of EXH can then be (38b), and exhaustification givesus (38c), which is the empirically correct result.

(38) a. F(S) = {work hard, watch TV, ¬watch TV, work hard ∧ ¬watch TV}b. A = {work hard, work hard ∧ ¬watch TV}.c. EXH(A)(S) = work hard ∧ ¬(work hard ∧ ¬watch TV).

The last example in (20), repeated in (39), works similarly, see (40).

(39) Bill is tall and not bald. John is (only) tall.Inference: ¬[John is tall and not bald]

(40) a. F(S) = {tall, bald, ¬bald, tall ∧ ¬bald}b. A = {tall, tall ∧ ¬bald}c. EXH(A)(S) = tall ∧ ¬(tall ∧ ¬bald)

3.2.3 The symmetry preserving cases

It remains to show that Atomicity does not allow us to break symmetry in the “sym-metry preserving” cases, i.e. in the examples in (21). Let us examine these, beginningwith (21a), repeated in (41).

(41) Bill ate exactly three cookies. John (only) ate three cookies.*Inference: ¬[John ate exactly three cookies]

The definition of F(S) by F&K, constrained by Atomicity, implies that (42) is the set offormal alternatives to S = John ate three cookies in this context. Note that applicationof Atomicity in this case is vacuous in the sense that the non-derivable alternativeexactly four can be excluded from A without violating the closure condition in (27c).

(42) F(S) = {three, exactly three, four}

To get the non-attested inference, we need the domain of EXH to be (43).

123


(43) {three, exactly three}

However, (43) does not qualify as A: F(S)\(43) contains four, which is in the Booleanclosure of (43), as four ≡ three ∧ ¬exactly three. Consequently, we predict that (41)cannot license the inference that it is not the case that John ate exactly three cookies,which is the correct prediction.22

The next example, (21b), is repeated in (44).

(44) Bill fathered children and no twins. John (only) fathered children.*Inference: ¬[John fathered some children and no twins]

It follows from Atomicity imposed on F(S) that the set of formal alternatives to S =John fathered some children is (45).23

(45) F(S) = {children, twins, children ∧ no twins, no twins}

To get the non-attested inference, we need the domain of EXH to be (46).24

(46) {children, children ∧ no twins}

Again, (46) does not qualify as A, since F(S)\(46) contains twins which, being equiv-alent to children ∧ ¬(children ∧ no twins), is in the Boolean closure of (46). Thus,we predict that (44) cannot license the inference that it is not the case that John fatheredchildren and no twins, i.e. that he fathered twins. This is the correct prediction.

The last example in (21) is repeated in (47).

(47) Bill passed some of the military fitness tests and failed some. John (only)passed some of the tests.*Inference: ¬[John passed some of the military fitness tests and failed some]

22 Note that (41) can, with some effort on the part of the hearer, be understood as implying that John ateexactly three cookies, in which case the sequence would sound odd by virtue of not being able to establisha difference between Bill and John (see footnote 4). One interpretation of this fact is that the effort inquestion is one of ignoring the contextually salient alternative (exactly three), keeping only the lexicalalternative (four) in F(S). It seems that in general, such an effort can be made, i.e. that inferences basedon contextually salient alternatives are optional (see footnotes 16 and 23 in Fox and Katzir 2011). Anotherexample illustrating the same point, brought to our attention by Jacopo Romoli (p.c.), is (i).

(i) Last year, some of my students passed the test. This year, in the same way, not all of them passed it.

Romoli points out, and we agree, that (i) can have the implicature that some of my students passed thetest this year. Again, this implicature is predicted to arise if F(not all) contains not some, generated bylexical replacement, but does not contain the contextually salient alternative some. (Adding in the sameway makes the sequence better, apparently because it then becomes clear that the two sentences are notmeant to express a contrast between last year and this year.)In this paper, we abstract away from the issue of optionality of contextually salient alternatives and

discuss the examples under the assumption that the relevant hearer does not make an effort to ignore suchalternatives.23 Without Atomicity, the set of formal alternatives to S would be (45) ∪ {no children}.24 The non-attested inference can also be obtained with another set being the domain of EXH, namely{children, children ∧ no twins, no twins}. However, this set has the same problem as (46), as the readercan easily verify.

123


The set of formal alternatives to John passed some of the tests, under the assumptionthat F(S) is constrained by Atomicity, is (48).

(48) F(S) = {pass some, pass all, fail some, fail all, pass some ∧ fail some}

To get the non-attested inference, we need the domain of EXH to be (49).25

(49) {pass some, fail some, fail all, pass some ∧ fail some}

However, (49) does not qualify as A, as F(S)\(49) contains pass all, which, beingequivalent to both pass some ∧ ¬fail some and pass some ∧ ¬(pass some ∧ failsome), is in the Boolean closure of (49). Consequently, wemake the correct predictionthat (47) cannot imply that it is not the case that John passed some of the tests andfailed some, i.e. that he passed all of the tests.

3.2.4 An apparent problem

An example which might appear problematic for the Atomicity account is (16), takenfrom F&K and repeated in (50).

(50) Detective A concluded that the robbers stole the book and not the jewelry.Detective B (only) concluded that they stole the book.Inference: ¬Detective B concluded that the robbers stole the book and not thejewelryInference: ¬Detective B concluded that the robbers stole the book and thejewelry

We have presented, in the same way we think F&K did, the second inference of (50)as a consequence of (51) being a formal alternative of the prejacent Detective Bconcluded that the robbers stole the book.

(51) Detective B concluded that the robbers stole the book and the jewelry

Given Atomicity, it turns out that (51) cannot be derived from the prejacent in thecontext provided by (50), as the derivation involves replacing a proper part of a syn-tactically atomic expressionwith another expression, as shown in (52). The substitutionsource in this case includes α = [AT the book and not the jewelry] and β = [AT thejewelry].

(52) Derivation of (51):

0. ... stole the book the prejacent1. ... stole [AT the book and not the jewelry] the book / α2. ... stole [AT the book and [AT the jewelry]] *not the jewelry / β

25 There are two other sets which will get us the non-attested inference, namely {pass some, fail some}and {pass some, pass some ∧ fail some}. However, both fail to qualify for A, for the same reason that (49)does.

123


However, there is another way for the inference in question to come about: by EXHnegating the alternative in (53), which can be derived from the prejacent, namely byreplacing the direct object the book in (51a) with β = [AT the jewelry].

(53) Detective B concluded that John stole the jewelry

Under the standard assumption that propositional attitude verbs such as concludedenote (restricted) universal quantifiers over worlds and thus distribute over conjunc-tion (cf. Hintikka 1969), if Detective B did not conclude that John stole the jewelry,then he did not conclude that John stole the book and the jewelry.26

4 Extending the proposal

4.1 Indirect implicature

In this sectionwewill consider how the proposal we justmade can be extended in somenatural fashion to derive some observations that have posed problems, specificallyovergeneration problems, for Neo-Gricean theories of scalar implicature. First, weshould note that the system, as it is, can already account for a puzzle, presentedin Romoli (2012a), which relates to the well-known observation that [not[all]], bydefault, implicates [some] (Atlas and Levinson 1981; Horn 1989; Sauerland 2004), asexemplified in (54).27

(54) The committee didn’t pass all of my students.Inference: ¬[The committee didn’t pass some of my students]

Romoli points out, correctly, that F&K’s structural characterization of alternativespredicts the attested inference of (54) to be non-existent.28 Thus, suppose the analysisof the prejacent S = the committee didn’t pass all of my students is (55).

26 A curious fact to note is that (i), which is the modal-less variant of (50), seems to have the obligatoryinference that John did not steal the jewelry, i.e. that John is no different from Bill, and hence sounds a littleodd (see footnote 4).

(i) Bill stole the book but not the jewelry. John (only) stole the book.

Given what we have said, this fact means that the set of alternatives to John stole the book in this contexthas to be A = {book, jewelry} and cannot be A′ = {book, book ∧ ¬jewelry, jewelry} or A′′ = {book,book ∧ ¬jewelry}: A′ would license no inference about the jewelry and A′′ would license the inferencethat John stole the jewelry. The reason why the set of alternatives cannot be A′ is most likely that this setcontains only elements which cannot be negated by EXH. We have no real answer as to why A′′ is notavailable as an option. We suspect the reason to be that the relevant pragmatic scale is missing (see thediscussion in Sect. 3.1). Whether or why that hypothesis is true is a question which we will have to leavefor future research.27 We let “[α[β]]” stand for sentences in which α c-commands β.28 More precisely, the problematic prediction is made by F&K’s theory in conjunction with the assumption,empirically motivated and built into the definition of EXH, that the computation of scalar implicaturesinvolves the negation of not only logically stronger but also logically independent alternatives (Spector2006).

123


(55) [TP PAST [NegP not [VP the committee pass all of my students]]]

F&K’s theory predicts both S′ = the committee didn’t pass some of my studentsand S′′ = the committee passed some of my students to be formal alternatives of(55): the first derived by replacing all with some and the second derived by replacingNegP with VP followed by replacing all with some. The problem, of course, is that S′and S′′ are symmetric alternatives, which means that (54) is predicted not to licensethe inference that the committee passed some of my students, which is the attestedinference of (54). On the contrary, the facts follow straightforwardly from Atomicity,which simply rules out S′′ as a formal alternative of S, because its derivation involvesreplacing a subpart of a syntactically atomic expression, namely VP, with another.29

Thus, Atomicity circumvents the overgeneration problem that F&K’s theory facesin this particular case, and in cases where a strong scalar item is embedded undernegation.30

4.2 The switching problem

Romoli (2012b) discusses another case of overgeneration which has to do with struc-tures in which a weak scalar item embeds a strong one, as exemplified in (56).

(56) Some of my students did all of the readings.*Inference: ¬[All of my students did some of the readings]

Intuitively, (56) does not have the implicature that it is not the case that all of mystudents did some of the readings, i.e. that some of my students did none of thereadings. This implicature is predicted if S′ = all of my students did some of thereadings is a formal alternative of the prejacent S = some of my students did allof the readings.31 Thus, what we need is for S′ not to be a formal alternative of S.Unfortunately, Atomicity does not rule out S′ as a formal alternative of S, since theformer can be derived from the latter without any AT-marked expression having itsproper parts replaced by another expression, as (57) shows. Note that the substitutionsource includes α = someAT and β = allAT.

29 Note that it is also impossible to derive S′′ from S by replacement of all with some followed byreplacement of NegP with the newly formed VP = the committee pass some of my students. The reasonis that this VP is not an element of the substitution source: it is neither a lexical item nor a constituent thathas been uttered in the context.30 Note, incidentally, that the success of our proposal in dealing with the puzzle of indirect implicatureprovides support for the definition of structural simplification in terms of substitutions alone (as in F&K andin the present paper) rather than in terms of substitutions and deletions (as inKatzir 2007).With substitutionsalone, NegP can only be simplified to eliminate negation by substituting VP for NegP, but then, Atomicitymandates that VP will be used as is, with no possibility of replacing all with some. This accounts for theunavailability of S′′. If deletions were allowed, there would be a way to derive the problematic S′′ withoutviolating Atomicity: simply delete not and then replace all with some. We thank Roni Katzir for drawingour attention to this point.31 Because S′ is logically independent of S and EXH negates logically independent alternatives (see (1)).

123


(57) Derivation of S′ from the prejacent S:0. Some of my student did all of the reading the prejacent1. Some of my student did someAT of the reading all / α2. AllAT of my student did someAT of the reading some / β

The puzzle, then, is that [some[all]] does not implicate ¬[all[some]], although[all[some]] is a (logically independent) formal alternative of [some[all]]. We mightimagine a condition which has the effect of preventing some and all to “switch places”in the derivation of a formal alternative. But an explanation along this line wouldfounder in the face of the following example.32

(58) None of my students did all of the readings.Inference: All of my students did some of the readings

Under the standard assumption that none, at the relevant level of analysis, is to bedecomposed into sentential negation taking scope over some, i.e. as [not[some]](cf. Penka 2011 and references therein), the observation in (58) can be represented asfollows.

(59) [not [some of my students did all of the readings]]Inference: ¬[not [all of my students did some of the readings]]

This inference is predicted by our account, as we predict [not[all[some]]] to be aformal alternative of [not[some[all]]] (the derivation of the former from the latter isthe same as (57) modulo the fact that every sentence is embedded under negation). Theproblem, then, is that [not[some[all]]] implicates ¬[not[all[some]]] but [some[all]]does not implicate ¬[all[some]], even though in both cases, the relevant alternativeis derivable from and logically independent of the prejacent. A more informal wayto frame the problem is the following: certain facts suggest that some and all can“switch places” only if both are embedded under negation, while we predict thatnegation makes no difference (hence the title of this subsection).

The solution to this problem, therefore, will consist in preventing the derivation of[all[some]] from [some[all]] without preventing the derivation of [not[all[some]]]from [not[some[all]]]. We propose to do this by adding to Atomicity the followingconstraints on the syntactic derivation of formal alternatives.33

32 According to an anonymous reviewer, the inference in (58) is “not compelling.” We agree that thisinference is rather weak, but believe that it is possible, concuring with the claim made in Romoli (2012a)based on experiments done in Chemla (2009). However, our aim here is to convince the reader that to theextent that the inference in question is licensed, it can be accounted for by an extension of our proposalwhich looks rather natural.33 Romoli (2012b) proposes a solution to the “switching problem” which has in common with the solutionwe set out below the stipulation that (i) replacement of scalar items should proceed from the bottom up and(ii) no such replacement may be weakening. The reader is invited to consult Chapter 6 in Romoli (2012b)for details. Romoli does not make use of AT-marking or any similar device, which we argue to be necessaryto explicate the notion of “replacement from the bottom up.” Furthermore, we do not see how his approachto the switching problem can be generalized to account for the other facts which we have discussed sofar.

123


(60) Constraints on the derivation of formal alternatives34

a. Only non-AT-marked expressions are replaceable.b. The most deeply embedded replaceable expression must be replaced

first.c. No replacement may yield a sentence which is logically weaker than the

prejacent.

Let us see how these constraints work. First, consider the case where the prejacent is[not[some[all]]]. We predict that the following derivation is possible.

(61) [not[some[all]]] the prejacent[not[some[someAT]]] all / someAT[not[allAT[someAT]]] some / allAT

Note that none of the steps result in a sentence logically weaker than the prejacent.Now consider the case where the prejacent is [some[all]]. Logically, there are twoways to derive the problematic [all[some]] from it; either as in (62) or as in (63).

(62) [some[all]] the prejacent[some[someAT]] *all / someAT[allAT[someAT]] some / allAT

(63) [some[all]] the prejacent[allAT[all]] *some / allAT[allAT[someAT]] all / someAT

It turns out that both derivations are excluded by the constraints in (61). In (62), thesecond step yields a sentence weaker than the prejacent, and in (63), the second stepreplaces a constituent which is not the most deeply embedded replaceable expressionsince all is replaceable and c-commanded by some.

We thus have a solution to the second overgeneration problem as well. It can beverified (though we won’t do so here) that the addition of the constraints in (61) toour proposal does not affect how it accounts for the facts discussed in the previoussections.

5 Summary

Wehaveproposed a characterization of formal alternativeswhich does justice to certainobservations, some of them novel, which pose a challenge for existing theories ofalternative generation. The structural constraints we propose on F(S) show intriguingparallels between the derivation of formal alternatives and the derivation of sentences.Both involve an initial set of expressions to be used, the “substitution source” in the case

34 While (60a) might seem more arbitrary than (60b), which says that the derivation of alternatives, likemany other syntactic processes, proceeds “bottom up,” and (60c), which makes clear functional sense, it isnot entirely without rationale: barring replacement of AT-marked expressions can be understood as barringvacuous replacement steps. Thus, (60a) rules out replacement of A with B followed by replacement of Bwith C, which amounts to the same as replacement of A with C.

123


of formal alternatives and the “numeration” in the case of sentences. Expressions in thesubstitution source are treated as syntactically atomic,making this construct essentiallya sort of numeration, albeit one that is contextually determined. The derivation offormal alternatives must proceed from the bottom up, with the relevant rule applyingto more deeply embedded constituents before applying to less deeply embedded ones.This condition makes the syntactic derivation of formal alternatives strikingly similarto the syntactic derivation of sentences, prompting the question of whether/to whatextent the former might be a “cooptation” of the latter. These are questions that wehope will be addressed in future research.

Acknowledgments We thank Luka Crnic, Danny Fox, Manfred Krifka, Clemens Mayr, Hazel Pearson,Sophie Repp, and Jacopo Romoli for fruitful discussion. We thank Roni Katzir, who reviewed this papernon-anonymously, for his many valuable critiques, and thank an anonymous reviewer for several helpfulsuggestions. Special thanks go to Danny Fox for recommending substantial changes to an earlier ver-sion of this paper. The present work is supported by a grant from the Deutsche Forschungsgemeinschaft(Sonderforschungsbereich 632, Projekt A2).

References

Atlas, J.D., and S.C. Levinson. 1981. It-clefts, informativeness, and logical form: Radical pragmatics.In Radical pragmatics, ed. P. Cole, 1–61. New York: Academic Press.

Chemla, E. 2009. Presuppositions of quantified sentences: Experimental data.Natural Language Semantics17(4): 299–340.

Chierchia,G.,D. Fox, andB. Spector. 2012. The grammatical viewof scalar implicatures and the relationshipbetween semantics and pragmatics. In Semantics: An international handbook of natural languagemeaning, ed. P. Portner, C. Maienborn, and K. von Heusinger, 2297–2332. Berlin: de Gruyter.

Chomsky, N. 1995. The Minimalist Program. Cambridge, MA: MIT Press.Crnic, L. 2012. Focus particles and embedded exhaustification. Journal of Semantics 30(4): 533–558.Fox, D. 2007a. Free choice disjunction and the theory of scalar implicatures. In Presupposition and

implicature in compositional semantics, ed. U. Sauerland and P. Stateva, 71–120. Basingstoke:Palgrave-Macmillan.

Fox, D. 2007b. Pragmatics in linguistic theory. MIT class notes.Fox, D., and R. Katzir. 2011. On the characterization of alternatives. Natural Language Semantics 19:

87–107.Groenendijk, J., andM. Stokhof. 1984. Studies on the semantics of questions and the pragmatics of answers.

PhD thesis, University of Amsterdam.Hintikka, J. 1969. Semantics for propositional attitudes. In Philosophical logic, ed. J.W. Davis et al., 21–45.

Dordrecht: Reidel.Horn, L. 1989. A natural history of negation. Chicago: The University of Chicago Press.Katzir, R. 2007. Structurally-defined alternatives. Linguistics and Philosophy 30: 669–690.Katzir, R. 2008. Structural competition in grammar. PhD thesis, MIT.Klinedinst, N. 2004. Only scalar only. Handout presented at the ‘Presupposition and Implicature’ workshop,

Paris.Krifka, M. 1995. The semantics and pragmatics of polarity items. Linguistic Analysis 25(3–4): 209–257.Kroch, A. 1972. Lexical and inferred meanings for some time adverbials. Quarterly Progress Reports of

the Research Laboratory of Electronics 104: 260–267.Lewis, D. 1988. Relevant implication. Theoria 54(3): 161–174.Magri, G. 2009. A theory of individual-level predicates based on blind mandatory scalar implicatures.

Natural Language Semantics 17(3): 245–297.Magri, G. 2011. Another argument for embedded scalar implicatures based on oddness in downward entail-

ing environments. Semantics and Pragmatics 4(6): 1–51. doi:10.3765/sp.4.6.Penka, D. 2011. Negative indefinites. Oxford: Oxford University Press.Romoli, J. 2012a. A problem for the structural characterization of alternatives. Unpublished manuscript,

Harvard University.

123

http://dx.doi.org/10.3765/sp.4.6


Romoli, J. 2012b. Soft but strong: Neg-raising, soft triggers, and exhaustification. PhD thesis, HarvardUniversity.

Rooth, M. 1992. A theory of focus interpretation. Natural Language Semantics 1: 75–116.Sauerland, U. 2004. Scalar implicatures in complex sentences. Linguistics and Philosophy 27(3): 367–391.Sauerland, U. 2012. The computation of scalar implicatures: Pragmatic, lexical or grammatical? Language

and Linguistic Compass 6: 36–49.Spector, B. 2006. Scalar implicatures: Local or global? Exhaustivity and Gricean reasoning. Unpublished

manuscript, Institut Jean Nicod, Paris.Spector, B. 2010. Scalar implicatures and grammar alternatives for focus and scalar implicatures (based on

Fox and Katzir). Handout for ESSLLI, Copenhagen.von Fintel, K., and I. Heim. 1997. Pragmatics in linguistic theory. MIT class notes.

123

Constraining the derivation of alternatives

Documents

Transcript of Constraining the derivation of alternatives